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Solved on Nov 07, 2023

Find the $r$ value for the equation $y=4.95 e^{0.0542 t}$ and explain the type of change it represents.

STEP 1

Assumptions1. The given equation is $y=4.95 e^{0.054 t}$ . . The equation is of the form $y=A e^{r t}$ .
3. We need to identify the $r$ value and explain the type of change it represents.

STEP 2

In the given equation, we can see that the $r$ value corresponds to the coefficient of $t$ in the exponent of $e$ .

STEP 3

By comparing the given equation $y=.95 e^{0.0542 t}$ with the standard form $y=A e^{r t}$ , we can identify $r$ .
$r =0.0542$

STEP 4

The $r$ value in the exponential function $y=A e^{r t}$ represents the rate of change.

STEP 5

In this context, a positive $r$ value indicates that the function is growing exponentially.The $r$ value for the equation is0.0542 and it represents an exponential growth.

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